Summary- True Parameter of VWN Functional of G98W

From: "TELKUNI" <telkuni &$at$& venus.dti.ne.jp>
Subject: Summary- True Parameter of VWN Functional of G98W
Date: Thu, 23 Aug 2001 00:56:41 +0900
Summary- True Parameter of VWN Functional of G98W
 Hello! CCLers
 A week ago, I posted the following question:
 >   I'm leaning the correlation functional "VWN " and try to use it
 on Gaussian98W.
 > I would like to know true G98W's VWN parameter.
 >
 >   According to the original paper of VWN (S. H. Vosko, L. Wilk, and M.
 Nusair: Can. J.
 > Phys. vol.58, 1200 (1980)), the functional employs the parameters as
 follows:
 > x0(x-zero) = -0.409286, b = 13.0720, c = 42.7298 (in Section4).
 >
 >  But the other books and articles, there are different combination of
 parameters,
 > for example(paramagnetic state): x0 = -0.10498, b = 3.72744, c = 12.9352
 (by Density
 > Functional Theory And Its Application - Japanese).
 >
 >   I think G98W might employ the original paper's parameters, but I don't
 know the
 > articles nor method to check it. If you know the method(for example: using
 IOp option)
 > or articles, please teach me.
 Thanks a lot for those who gave me the instructions and helpful information.
 Here I summarize them. And I hope it will be helpful to some others.
 === [1] from Leticia Gonzalez Herrero  ===
 The straight forward way to know what is implemented in G98 is to check
 the code.
 Good luck.
 >Telkuni:   It is right, but difficult for me.
 === [2] from Christoph van Wuellen ===
 1.) Gaussian VWN functional uses the parameters given in *table* 3 of
 the VWN paper. These parameters approximate the RPA results, not the
 Monte-Carlo results! These parameters are used for the closed-shell and
 completely spin-polarized (only alpha spin electrons) cases.
  >Telkuni: ---CRRECTION---
  The parameters are in the text discussing table 3, on page 7, left column,
  after equation 4.4:
   x0 -> -0.409286  b  ->  13.0720   c  -> 42.7198   (Paramagnetic Case)
   x0 -> -0.743294  b  ->  20.1231   c  -> 101.578   (Ferromagn. Case)
  The functional derived from these parameters duplicates the g98 results.
 2.) Gaussian VWN does not use the RPA spin stiffness parameters to inter-
 polate between these two cases, but uses the interpolation valid for the
 exchange energy of a uniform electron gas. (I do not know what happened that
 they chose this option).
 With the TZ basis sets of Ahlrichs and Schafer you should get the following
 energies
 Atom:   He(ground state)   He(1s2s Triplet)      N Atom(Quartet)
 HF       -2.85989543        -1.79100228           -54.40232895
 LDA3     -2.86994363        -1.77391426           -54.26495985
 LDA5     -2.83256107        -1.73613023           -54.13356852
 BLYP     -2.90460692        -1.79477978           -54.58993091
 B3LYP    -2.91302754        -1.80220154           -54.60420134
 Things to note:
 (1) open shell calculations done spin-unrestricted. Hartree-Fock results
      given for comparison (if they do not agree, something is wrong with
      the basis set).
 (2) The three examples cover the three cases (spin-unpolarized, completely
      spin-polarized, partially spin-polarized) mentioned above (the inter-
      polation problem only shows up for the N atom).
 (3) LDA3 = the LDA functional implemented in Gaussian
      LDA5 = the LDA functional used by the rest of us (i.e. SVWN5 in G98)
 (4) B3LYP contains LDA3 (I guess this is the right choice, since B3LYP was
      'invented' by the Gaussian developers).
 (5) I implemented these functionals in my own program and got the same
      results, the only way to *really* know what is implemented in G98.
 (6) I suggest that my numbers are checked by others, so that our community
      knowns which functional is which. Please use highly accurate numerical
      grids. If the reference numbers should be obtained with another basis
      set, please make a suggestion.
 === [3] from Matt Challacombe ===
 Right, you will want to have a look at the very helpfull paper:
   &$at$& article{Hertwig97,
         author = {R. H. Hertwig  and W. Koch},
         title = {On the parameterization of the local correlation functional.
                  What is Becke-3-LYP?},
         journal = {Chem. Phys. Lett.},
         year = {1997 },
         volume = 268,
         number = {5-6},
         pages = {345-351},
         month = {APR 18}
  }
 === [4] from Van Dam, HJJ (Huub) :  Opinion on reply [2] ===
 The problem discussed here is typical for some issues related to DFT
 calculations: How do you know what a program actually calculates when
 you ask for a certain functional (e.g. B3LYP). This problem can be
 tackled by collecting highly accurate reference data, complete
 mathematical definitions of the functionals, and finally actual
 implementations of functionals. We have now a collection of  functionals
 and associated data available online at
     http://www.dl.ac.uk/DFTlib
 With respect to the B3LYP question we agree with Christoph van Wuellen
 that the Gaussian implementation is the right one because they
 'invented' it. An implementation and associated reference data of the
 functional equivalent to the one in Gaussian is given on our website.
 The reference to Stephens et al. (1994) is the original reference to
 B3LYP, the confusion around the VWN part was later clearified by Hertwig
 and Koch (1997). The findings of Hertwig and Koch are reflected in the
 Gaussian online technical documentation (Frisch et al., 1998).
   Huub van Dam.
 > 1.) Gaussian VWN functional uses the parameters given in *table* 3 of
 > the VWN paper. These parameters approximate the RPA results, not the
 > Monte-Carlo results! These parameters are used for the closed-shell and
 > .....
  Thank you very much.
 ------------------------------------------------
                Telkuni Tsuru
   Kyushyu Electronic Technology and Research
           telkuni &$at$& venus.dti.ne.jp
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